Question

Find the missing number in this simplified exponential expression: 15 to the power of ?÷15 to the power of 7=15 to the power of 12
.(1 point)
Responses

19
19

−19
negative 19

5
5

−5

Answers

Answered by GPT-4o mini
To solve the equation \( \frac{15^?}{15^7} = 15^{12} \), we can use the properties of exponents.

Using the quotient rule of exponents, we have:

\[
\frac{15^a}{15^b} = 15^{a-b}
\]

So, applying that to our equation:

\[
15^{? - 7} = 15^{12}
\]

Since the bases are the same, we can set the exponents equal to each other:

\[
? - 7 = 12
\]

Now, we can solve for \( ? \):

\[
? = 12 + 7
\]
\[
? = 19
\]

Therefore, the missing number is:

**19**
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